Journal of Mathematical Sciences & Computational Mathematics最新文献

{"title":"INVESTIGATION INTO THE CHALLENGES FACING PLANNING OF MATHEMATIC PROGRAMME IN SENIOR SECONDARY EDUCATION IN ABUJA, NIGERIA","authors":"Ogunode Niyi Jacob","doi":"10.15864/jmscm.2102","DOIUrl":"https://doi.org/10.15864/jmscm.2102","url":null,"abstract":"The aim of this study is to investigate the challenges facing the planning of mathematics programme in Federal Capital Territory, Nigeria. The study adopted descriptive research survey design. The population of the study comprised ninety (90) respondents. Stratified and systematic sampling\u0000 technique was used to select the sample population. The study employed the used of questionnaire as instrument for data collection. Two lecturers from Educational Administration and planning from University of Abuja was consulted to validate the questionnaire. Three research questions and\u0000 two hypotheses were developed for the study. Test-retest reliability was employed for the study. Percentage and Chi-square test was used to test the hypotheses and data collected from the study. The result revealed that there are challenges facing the planning of mathematics programme of senior\u0000 secondary education and the challenges includes; inadequate data/information to plan, inadequate funding of planning of mathematics programme, poor capacity development of few mathematics planners, inadequate professional mathematics planners ,political instability, corruption and lack of\u0000 political will to support planning of mathematics education. The study concluded that the implication of the challenges on the implementation mathematics education is poor implementation of the mathematics programme in the senior secondary schools. The study recommends that the government\u0000 should increase the funding of educational planning in the country especially mathematics education.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121215517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"RECREATIONAL MATHEMATICS","authors":"A. Chatterjee","doi":"10.15864/jmscm.1407","DOIUrl":"https://doi.org/10.15864/jmscm.1407","url":null,"abstract":"Over centuries mathematicians have generated a wealth of rigorous and high level mathematics that is the armoury of pure mathematicians. But there is an interesting segment of mathematics that can justifiably be consigned to a different realm, which is the world of recreational mathematics.\u0000 In this paper we will visit a few interesting areas of this fascinating domain.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121375662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"USE OF LINEAR ALGEBRA AND PARTIAL DERIVATIVES IN SUPERVISED LEARNING (ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING)","authors":"Prerana Misra, Avik Mukherjee, Anish Pyne","doi":"10.15864/jmscm.1305","DOIUrl":"https://doi.org/10.15864/jmscm.1305","url":null,"abstract":"When we talk about new technologies and the advancement in the field of Computer Science, the first thing that comes to our mind is Artificial Intelligence and Machine Learning. Artificial Intelligence has seen resurgence in the 21st century because of its ability to mimic\u0000 functions done by human intelligence like “problem solving” and “learning”. It is slowly becoming the area of interest of the new generation because of its modern capabilities which even human intelligence struggle to perform like competing at highest level in strategic\u0000 game systems, intelligent routing, operating cars autonomously and simulations. Artificial Intelligence may look easy but there are several tools involved in making it successful. One of the main tool is “Statistical Methods”. Linear algebra and Partial Differential Equations have\u0000 become the base of this field. The objective of our paper is to throw light on how Statistical Methods and Mathematical optimization provide the base for the working of Supervised Learning. Over years, algorithms inspired by Partial Differential Equations (PDE) and Linear Algebra have had\u0000 an immense impact on many processing and autonomously performed tasks that involve speech, image and video data. Image processing tasks and intelligent routing done using PDE models has lead to ground-breaking contributions. The reinterpretation of many modern machine capabilities like artificial\u0000 neural networks through PDE lens has been creating multiple celebrated approaches that benefit a vast area. In this paper, we have established some working of these methods in different subfields of Artificial Intelligence. Guided by well-established theories we demonstrate new insights and\u0000 algorithms for Supervised Learning and demonstrate the competitiveness of different numerical experiments used in the sub-fields. Not only will we see the wide application of Artificial intelligence but also its ability to slowly replace human works leading to unemployment which are part of\u0000 its limitation. This research will provide wider insights into the multiple mathematical processes which acts as roots to make the field of Computer Science interesting and successful.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133585217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"CRYPTOGRAPHY","authors":"B. Ghosh, Rohit Aich, Arka Khag, S. Nayak, Prashant Kumar","doi":"10.1002/9781119533245.ch13","DOIUrl":"https://doi.org/10.1002/9781119533245.ch13","url":null,"abstract":"The word cryptography was coined from two Greek words ‘Krypto’, meaning hidden and ‘graphein’ meaning writing. Thus, cryptography means hidden writing. Cryptography is the method of protecting important data and information from third parties called adversaries\u0000 or the public. It is also known as encryption. Modern cryptography is basically based on Mathematics and Computer science. The roots of cryptography are found in Roman and Egyptian civilizations. Hieroglyph is the oldest cryptographic technique. Based on security needs and threats, various\u0000 cryptographic methods such as symmetric key cryptography, public key, private key, microdots, etc are adopted [1]. It is a two step process; encryption and decryption. The encryption process uses a cipher (code) in order to encrypt plaintext and convert it into ciphertext. Decryption is the\u0000 opposite of encryption that is to decode the encrypted message or information. Cryptography was used extensively in the American Revolutionary War, the First World War and the Second World War. For example if the code was ‘CVVCEM’ then it would mean ‘ATTACK’. The initials\u0000 of each letter is shifted by two places. This paper is basically a survey paper and we have studied the importance, features, advantages, and disadvantages and authenticated on the topic cryptography. Note: This paper is a REVIEW PAPER.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122608411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MATHEMATICS FOR MACHINE LEARNING","authors":"Gaurav Kumar, Rishav Banerjee, Deepak Kr Singh, Nitesh Choubey, Arnaw","doi":"10.15864/jmscm.1208","DOIUrl":"https://doi.org/10.15864/jmscm.1208","url":null,"abstract":"Machine learning is a way to study the algorithm and statistical model that is used by computer to perform a specific task through pattern and deduction [1]. It builds a mathematical model from a sample data which may come under either supervised or unsupervised learning. It is closely\u0000 related to computational statistics which is an interface between statistics and computer science. Also, linear algebra and probability theory are two tools of mathematics which form the basis of machine learning. In general, statistics is a science concerned with collecting, analysing, interpreting\u0000 the data. Data are the facts and figure that can be classified as either quantitative or qualitative. From the given set of data, we can predict the expected observation, difference between the outcome of two observations and how data look like which can help in better decision making process\u0000 [2]. Descriptive and inferential statistics are the two methods of data analysis. Descriptive statistics summarize the raw data into information through which common expectation and variation of data can be taken. It also provides graphical methods that can be used to visualize the sample\u0000 of data and qualitative understanding of observation whereas inferential statistics refers to drawing conclusions from data. Inferences are made under the framework of probability theory. So, understanding of data and interpretation of result are two important aspects of machine learning.\u0000 In this paper, we have reviewed the different methods of ML, mathematics behind ML, its application in day to day life and future aspects.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117136090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ANALYSIS OF THE TRANSMISSION DYNAMICS FOR ZIKA VIRUS WITH NONLINEAR FORCE OF INFECTIONS","authors":"Ezeama Chidi, Nwadibia Anthony Ifeanyi., Inyama Simeon Chioma, O. Andrew, Godwin Emeka Chigaemezu","doi":"10.15864/jmscm.1201","DOIUrl":"https://doi.org/10.15864/jmscm.1201","url":null,"abstract":"This paper presents a seven-dimensional ordinary differential equation of mathematical model of zika virus between humans and mosquitoes population with non-linear forces of infection in form of saturated incidence rate. Vertical transmission is introduced into the model. These incidence\u0000 rates produce antibodies in response to the presence of parasite-causing zika virus in both human and mosquito populations. The existence of region where the model is epidemiologically feasible is established (invariant set) and the positivity of the models is also established. The basic properties\u0000 of the model are determined including the reproduction number of both cases, R0 and R0 |p=q=0 R respectively. Stability analysis of the disease-free equilibrium is investigated via the threshold parameter (reproduction number R0\u0000 |p=q=0) obtained using the next generation matrix technique. The special case model results shown that the disease-free equilibrium is locally asymptotical stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Under specific conditions\u0000 on the model parameters, the global dynamics of the special case model around the equilibra are explored using Lyapunov functions. For a threshold parameter less than unity, the disease-free equilibrium is globally asymptotically stable. While the endemic equilibrium is shows to be globally\u0000 asymptotically stable at threshold parameter greater than unity. Numerical simulations are carried out to confirm the analytic results and explore the possible behavior of the formulated model. The result shows that, horizontal and vertical transmission contributes a higher percentage of infected\u0000 individuals in the population than only horizontal transmission.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130675893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Union of Brain Computer Interface and Internet of Things: An Integrated Platform to Enhance Cognitive Interaction in Real-time","authors":"Aritra Mukherji, N. Ganguli","doi":"10.15864/jmscm.1105","DOIUrl":"https://doi.org/10.15864/jmscm.1105","url":null,"abstract":"Brain Computer Interface (BCI) is a platform which receives brain signals, measures and analyses them, providing a pathway for the human brain to interact with external utilities in real-time. It is entirely independent of the normal output of peripheral nerves and muscles. On the other\u0000 hand, with the exposure of Internet of Things, the concept of connectivity of devices has evolved. The number of connected devices is expected to grow phenomenally across multiple industries, thereby boosting productivity and efficiency in coming years. This paper elaborates the procedure\u0000 of developing a system merging Brain Computer interface and internet of things, the possible applications of human-thing cognitive interactivity and the challenges we face while working with it.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117303668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"THE FORMULA nCr REVISITED","authors":"Soumendra Nath Banerjee","doi":"10.15864/jmscm.1109","DOIUrl":"https://doi.org/10.15864/jmscm.1109","url":null,"abstract":"A formula expressing nCr in summation form is formulated by the use of algorithmic counting techniques. Initially, a general counting problem is mathematically modeled and its solution is given by a formula derived using algorithmic counting. Thus, by generalization\u0000 a formula for nCr as a series is obtained.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122499217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A MATHEMATICAL MODEL TO STUDY THE EFFECT OF POROUS PARAMETER ON BLOOD FLOW THROUGH AN ATHEROSCLEROTIC ARTERIAL SEGMENT HAVING SLIP VELOCITY","authors":"Sibashis Nanda, Sayudh Ghosh, Ronit Chaudhury","doi":"10.15864/jmscm.1103","DOIUrl":"https://doi.org/10.15864/jmscm.1103","url":null,"abstract":"This theoretical investigation focusses on blood flow through a multiple stenosed human artery under porous effects. A mathematical model is developed for estimating the effect of porous parameter on blood flow taking Harschel-Bulkley fluid model (to account for the presence of erythrocytes\u0000 in plasma) and artery as circular tube with an axially non-symmetric but radially symmetric mild stenosis. The mathematical expression for the geometry of the artery with stenoses is given by the polynomial function model. The velocity slip condition is also given due weightage in the investigation.\u0000 It is necessary to study the blood flow through such type of stenosis to improve the arterial system. An extensive quantitative analysis is carried out by performing large scale numerical computations of the measurable flow variables having more physiological significance. The variations of\u0000 velocity profile, volumetric flow rate and pressure gradient with porous parameter are calculated numerically by developing computer codes. Their graphical representations with appropriate scientific discussions are presented at the end of the paper.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"379 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120981249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PROBABILITY IN MULTIVERSE","authors":"Supratik De","doi":"10.15864/jmscm.1108","DOIUrl":"https://doi.org/10.15864/jmscm.1108","url":null,"abstract":"Probability on itself is a hypothesis. It is defined as the chance of occurrence of an event out of the possible number of outcomes in a sample space. But things can slightly change if we take into account the concept of multiverse, as the existence of multiverse itself is probabilistic\u0000 and the occurrence of an event and its outcomes can’t be known and judged practically. Statistics is the most beloved child of mathematics, which has a lot of question everyday on various data. But here, it too may suffer difficulties as you don’t even know specifically all the\u0000 data.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122260857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}